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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Evolution of structure for direct control optimization

100%
Szymkat M., Korytowski A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2007
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tom 27
|
nr 1
165-193
EN
The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and flat generations are described in detail and illustrated with computational examples.
2
Content available remote

Remarks about energy transfer in an RC ladder network

80%
Mitkowski W.
International Journal of Applied Mathematics and Computer Science
|
2003
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tom 13
|
nr 2
193-198
EN
The problem of energy transfer in an -ladder network is considered. Using the maximum principle, an algorithm for constructing optimal control is proposed, where the cost function is the energy delivered to the network. In the case considered, optimal control exists. Numerical simulations were performed using Matlab.
3
Content available remote

A quadratic optimal control problem for a class of linear discrete distributed systems

80%
Rachik M., Lhous M., Kahlaoui O. E.
International Journal of Applied Mathematics and Computer Science
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2006
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tom 16
|
nr 4
431-440
EN
A linear quadratic optimal control problem for a class of discrete distributed systems is analyzed. To solve this problem, we introduce an adequate topology and establish that optimal control can be determined though an inversion of the appropriate isomorphism. An example and a numerical approach are given.
4

Viability theorems for stochastic inclusions

80%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
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tom 15
|
nr 1
61-42
EN
Sufficient conditions for the existence of solutions to stochastic inclusions $x_t - x_s ∈ ∫^t_s F_τ(x_τ)dτ + ∫^t_s G_τ(x_τ)dw_τ + ∫^t_s∫_{IRⁿ} H_{τ,z}(x_τ)ν̃ (dτ,dz)$ beloning to a given set K of n-dimensional cádlág processes are given.
5
Content available remote

Convergence of the Lagrange-Newton method for optimal control problems

80%
Malanowski K. D.
International Journal of Applied Mathematics and Computer Science
|
2004
|
tom 14
|
nr 4
531-540
EN
Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case, conditions for well-posedness and local quadratic convergence are given. The scope of applicability is briefly discussed.
6
Content available remote

Optimizing the linear quadratic minimum-time problem for discrete distributed systems

80%
Rachik M., Abdelhak A.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 2
153-160
EN
With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N, u) which minimizes J.
7
Content available remote

NTGsim: a graphical user interface and a 3D simulator for nonlinear trajectory generation methodology

80%
Di Trapani L., Inanc T.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
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nr 2
305-316
EN
Nonlinear Trajectory Generation (NTG), developed by Mark Milam, is a software algorithm used to generate trajectories of constrained nonlinear systems in real-time. The goal of this paper is to present an approach to make NTG more userfriendly. To accomplish this, we have programmed a Graphical User Interface (GUI) in Java, using object oriented design, which wraps the NTG software and allows the user to quickly and efficiently alter the parameters of NTG. This new program, called NTGsim, eliminates the need to reprogram the NTG algorithm explicitly each time the user wishes to change a parameter.
8
Content available remote

On an optimal control problem for a quasilinear parabolic equation

80%
Farag S. H., Farag M. H.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 2
239-250
EN
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
9

Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion

80%
You Y.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
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tom 16
|
nr 1
5-41
EN
Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient control problem in Hilbert spaces. The global existence and regularity of solutions of the state equation, the existence of optimal control, and the maximum principle as a necessary condition satisfied by optimal control are proved. By proving the local Lipschitz continuity of the value functions and by using lower Dini derivatives, an optimal synthesis (i.e. optimal feedback control) is obtained via solving a differential inclusion.
10
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Content available

Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control

80%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2013
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tom 33
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nr 1
89-109
EN
In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.
11
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Content available

A multidimensional singular stochastic control problem on a finite time horizon

80%
Boryc M., Kruk Ł.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2015
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tom 69
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nr 1
EN
A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.
12
Content available remote

Optimal control for a class of compartmental models in cancer chemotherapy

80%
Świerniak A., Ledzewicz U., Schättler H.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
|
nr 3
357-368
EN
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.
13
Content available remote

The linear programming approach to deterministic optimal control problems

80%
Hernández-Hernández D., Hernández-Lerma O., Taksar M.
Applicationes Mathematicae
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1996-1997
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tom 24
|
nr 1
17-33
EN
Given a deterministic optimal control problem (OCP) with value function, say $J^*$, we introduce a linear program $(P)$ and its dual $(P^*)$ whose values satisfy $\sup(P^*) \leq\inf(P)\leq J^*(t,x)$. Then we give conditions under which (i) there is no duality gap
14
Content available remote

A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

80%
Rafajłowicz E., Styczeń K., Rafajłowicz W.
International Journal of Applied Mathematics and Computer Science
|
2012
|
tom 22
|
nr 2
313-326
EN
Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.
15
Content available remote

On the discrete time-varying JLQG problem

80%
Czornik A., Świerniak A.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 2
203-207
EN
In the present paper optimal time-invariant state feedback controllers are designed for a class of discrete time-varying control systems with Markov jumping parameter and quadratic performance index. We assume that the coefficients have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Moreover, following the same line of reasoning, an adaptive controller is proposed in the case when system parameters are unknown but their strongly consistent estimators are available.
16
Content available remote

The gradient projection method for solving an optimal control problem

80%
Farag M. H.
Applicationes Mathematicae
|
1996-1997
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tom 24
|
nr 2
141-147
EN
A gradient method for solving an optimal control problem described by a parabolic equation is considered. The gradient projection method is applied to solve the problem. The convergence of the projection algorithm is investigated.
17
Content available remote

On directional change and anti-windup compensation in multivariable control systems

80%
Horla D.
International Journal of Applied Mathematics and Computer Science
|
2009
|
tom 19
|
nr 2
281-289
EN
The paper presents a novel description of the interplay between the windup phenomenon and directional change in controls for multivariable systems (including plants with an uneven number of inputs and outputs), usually omitted in the literature. The paper also proposes a new classification of anti-windup compensators with respect to the method of generating the constrained control signal.
18
Content available remote

Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem

80%
Idczak D., Majewski M., Walczak S.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 1
29-44
EN
In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
19
Content available remote

An optimal sliding mode congestion controller for connection-oriented communication networks with lossy links

80%
Bartoszewicz A., Leśniewski P.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 1
87-97
EN
A new discrete-time sliding-mode congestion controller for connection-oriented networks is proposed. Packet losses which may occur during the transmission process are explicitly taken into account. Two control laws are presented, each obtained by minimizing a different cost functional. The first one concentrates on the output variable, whereas in the second one the whole state vector is considered. Weighting factors for adjusting the influence of the control signal and appropriate (state or output) errors are incorporated in both the functionals. The asymptotic stability of the closed-loop system is proved, and the conditions for 100% bottleneck node bandwidth utilization are derived. The performance of the proposed algorithm is verified by computer simulations.
20
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Optimal control of systems determined by strongly nonlinear operator valued measures

71%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2008
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tom 28
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nr 1
165-189
EN
In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure mapping Σ × V to V* with Σ denoting the sigma algebra of subsets of the set I and f is a nonlinear operator mapping I × H to H, γ is a countably additive bounded positive measure and the control u is a suitable vector measure. We present existence, uniqueness and regularity properties of weak solutions and then prove the existence of optimal controls (vector valued measures) for a class of control problems.
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